Question

Cho biểu thức E=\(\left(\dfrac{\sqrt{x}+1}{\sqrt{x}-1}-\dfrac{\sqrt{x}-1}{\sqrt{x}+1}+4\sqrt{x}\right):\left(\sqrt{x}-\dfrac{1}{\sqrt{x}}\right)\)

a) Rút gọn biểu thức E

b) Tinh gia tri cua E khi x=(4+\(\sqrt{15}\))(\(\sqrt{10}-\sqrt{6}\))\(\sqrt{4-\sqrt{15}}\)

Answer 1

a: \(E=\dfrac{x+2\sqrt{x}+1-x+2\sqrt{x}-1+4\sqrt{x}\left(x-1\right)}{x-1}:\dfrac{x-1}{\sqrt{x}}\)

\(=\dfrac{4\sqrt{x}+4x\sqrt{x}-4\sqrt{x}}{x-1}\cdot\dfrac{\sqrt{x}}{x-1}\)

\(=\dfrac{4x^2}{\left(x-1\right)^2}\)

b: \(x=\left(4+\sqrt{15}\right)\cdot\left(\sqrt{5}-\sqrt{3}\right)\cdot\sqrt{8-2\sqrt{15}}\)

\(=\left(4+\sqrt{15}\right)\left(8-2\sqrt{15}\right)\)

\(=32-8\sqrt{15}+8\sqrt{15}-30=2\)

Thay x=2 vào E, ta được: 

\(E=\dfrac{4\cdot2^2}{\left(2-1\right)^2}=16\)